Solved – Why proc mixed give different DF than proc glimmix

degrees of freedommixed modelrepeated measuressas

I am trying to move data analysis from proc mixed to glimmix for the easy of the ilink transformation. However I am finding a big difference on the denominator DF when using either of them. As background. My data comes from a group of 95 calves that were fed 4 diets (about 24 calves per diet), my measure is neutrophil number in blood which was repeated 4 times (7, 14, 28, 42 d of age). Thus I am using sp (pow) as cov structure.
When using proc mixed with next statements: I got about 85 DF for the diff contrasts

CLASS calf diet parity sex age;
MODEL  RBCx=  diet sex age diet*sex diet*age  sex*age diet*sex*age / DDFM=KR;;
random calf (diet*sex);
repeated age /type=sp(pow)(age)  subject=calf (diet*sex) ;

However when using proc glimmix, for same contrast I got 336 DF when using next:

proc glimmix data = CBC_2011 IC= PQ;
CLASS calf diet parity sex age;
MODEL  RBCx=  diet sex age diet*sex diet*age  sex*age diet*sex*age / dist=Gaussian DDFM=KR;;
random age /type=sp(pow)(age)  subject=calf (diet*sex) residual;

Thanks in advance.
Miriam

Best Answer

In the mixed procedure code you specified a random statement and a repeated statement. The first one affects the G-matrix (and therefore the DFs), the second only affects the R-matrix. Your glimmix procedure code only contains a random statement with a residual option which therefore only affects the R-matrix and acts as the repeated statement in the mixed procedure. I think for proc glimmix you need a second random statement identical to the random statement of the mixed procedure.

In reply to Mike's comment I try to clarify the notation: The normal mixed model (proc mixed) can be written as: $ y=X \alpha + Z \beta + e$, where $\alpha$ represents the fixed effects and $\beta$ the random effects with $\beta \sim N(0, G)$ and $var(e)=R$, so that $var(y)=V=ZGZ' +R$.

In the generalized linear mixed model (proc glimmix) this is analogous: $y=\mu+e$, where $g(\mu)=X \alpha + Z \beta$, $var(e)=R$ and therefore $var(y)=V=var(\mu)+R \approx BZGZ'B +R$, $B$ being a diagonal matrix of variance terms.

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